EDIT: It's worth noting that in these cases the staff in question also had clear evidence in the form of signed reviews rating them that they were performing well. E.g. the guy I spent most time on a performance improvement plan for was ranked "exceeds expectations" in every criteria three years in a row while I was there, and was given 15%+ raises each of those years. This was in Europe, but for a US company.
I was the recipient of a PIP at my last job, went through the improvement process, and at the end of it, my manager signed off that my performance had returned to acceptable levels. I left about a month later.
So why am I not still there? Well, in the process of going through the PIP and asking myself how I let things get to that point, I realized that I was quite capable of excelling at everything I was supposed to be doing, but I just didn't give a shit anymore. My subconscious had already checked out of that job and was telling me it was time to move on.
When I realized that, my reaction was to start looking for another job while bringing my performance back to a good level. We quit on good terms: they "hired" me back to consult on some problems that came up after I left; I helped someone transition into my old position and I have a job better suited to my personality.
The right thing to do is to take the paperwork and say, "thanks, can you give me a few days to review this?" and stall as much as possible while looking for another job.
If you're feeling especially ballsy (and very confident in your ability to find another job quickly) you can say, "I'm not familiar with these at all, and my grandpa (R.I.P) always told me to get everything reviewed by an attorney before signing it, so that's what want to do. Is that OK?"
There is no self-improvement.
From experience (as a bystander), what really happens in a case like this is:
* Employee is terminated
* Employee believes they were terminated for a reason forbidden by state or federal law
* Employee retains an employment lawyer, who drafts a letter demanding compensation for the improper termination, citing specific claims of (say) sexual harassment, complaints articulated to superiors and to HR, and subsequent retaliatory firing.
* Employee does not necessarily prove those claims; they need only demonstrate sufficient facts and allegations to ensure that a lawsuit would not easily be dismissed.
* Employer almost invariably settles.
The two cases where employers don't settle:
* Employer is stupid, and believes that they will pay less to litigate a wrongful termination case than to settle.
* Employer is smart, and has an HR department that keeps excruciatingly careful records of things like sexual harassment complaints, alleged racially-tinged comments, ratio of black/white hires to black/white applications, &c, and is prepared to make it clear to employee's lawyer that the case will cost too much to pursue.
If you've ever wondered why smart employers go fucking apeshit when people make racially-tinged jokes, or why it's not necessarily in your best interests to bring your concerns to HR unless your game plan is to bring a wrongful termination complaint, there you go.
This is also the reason why, despite at-will status in basically every locale where you can hire people, "Performance Improvement Plan" is a euphemism for "slow-motion termination". The purpose of a PIP is to establish in the written record that an employee is a non-performer, so that when they're terminated, the employer can present evidence that there were reasons other than retaliation or discrimination.